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Abstract

Universals appear in a number different forms, from naturally occurring mathematical universals like the Fibonacci series, phi, and fractal scaling, to aesthetic universals like the golden ratio in architecture and other facets of human behavior like dance and religious belief. Music is another example of a powerful human universal. Further, within music there are a number of statistical regularities that have been empirically observed nearly universally. One such example would be the division of the octave into 12 equidistant tones. There are also a number of universal regularities that pertain specifically to melodic phrasing. This paper will examine four such statistical regularities of melodic phrases: namely, that there is an increased prevalence of smaller intervals over larger intervals (defined as Rule 1 throughout this dissertation), that larger intervals tend to ascend and smaller intervals tend to descend (defined as Rule 2 throughout this dissertation), that the overall contour of melodic phrases tend to ascend and then descend (defined as Rule 3 throughout this dissertation), and that melodic phrases tend to end on the tonic note (defined as Rule 4 throughout this dissertation). Here I look at the aggregate influence of these four regularities in melodic phrases, as they have hereto only been studied individually. In an initial series of experiments, labeled throughout this dissertation as Experiments1A, 1B, 1C, and 1D, attempt to determine the degree that these regularities collectively and individually influence people’s melodic preferences, their perception of well formed-ness, and their ratings of the interestingness of a series of artificially generated melodies that follow or violate the four melodic regularities to different degrees and in different combinations. In a further set of experiments, labeled throughout this paper as Experiments 2A and 2B, I will test which, if any, of these regularities can be explicitly identified by experimental subjects. Lastly, in Experiment 3, I tested how malleable melodic preferences are, and whether people’s preferences can be influenced or changed by exposure to certain types of melodic phrases – specifically, whether melodies that are in general rated low on aesthetic appeal can come to be regarded as more appealing through repeated exposure.

In order to test these questions, I have generated a large bank of 16-note melodic phrases (64 in total) representing each of the four aforementioned regularities and their combinations. In these artificially generated melodies, all notes were rhythmically consistent, with all notes being quarter notes. All melodies were also in the key of C Major and played at 120 beats per minute. The various melodies can be quantitatively operationalized along the lines of the extent to which they follow or violate each of the four regularities. Across the whole set of melodies, all possible combinations of rule following or rule violation are explored. This provides a substantially varied set of melodic stimuli for individuals to respond to, with control over many remaining aspects of the melodies (e.g., key, rhythm, tempo, dynamics, harmony, timbre), for the purposes of assessing the influence and importance of each of these regularities on aesthetic response.

First, in Experiment 1A, I wanted to determine the possible predictive power of each of these rules both individually and in combinations. In order to do that, I piggybacked on a method used by Reber (1969) in his research into implicit learning. Reber’s technique involved exposing people to a pool of stimuli demonstrating a certain statistical regularity or regularities (i.e., pseudo-words generated with a Markov chain) during a learning phase, then exposing them to stimuli that either adhere to or violate the regularity or regularities to which they were exposed, and to elicit their ratings along a few possible dimensions. In this present case, since people generally accumulate a large amount of musical experience simply by exposure and listening over the course of their lives (unlike the Reber studies that involve a learning phase to expose people to the rules governing the artificial system), an experiment that tests musical regularities would not need such a learning phase, as that has already occurred over the course of the lives of the participants.

Therefore, in Experiment 1A, participants were simply exposed to a few examples of each of the melodic rule combinations; after each melody, they were asked to rate the phrase’s well-formedness, preference, and interestingness. In other words, after hearing each melody people specified how well-formed the phrase seemed, how interesting the phrase was, and their preference for the melody, along a seven-point Likert scale. The results of this study were first used to examine the possible correlations between these various three dependent measures of well-formedness, preference, and interestingness dependent upon the combination of the phrase regarding the four regularities being used here. As all of the variables showed high positive intercorrelations, they were combined via a principal components analysis, and the resulting factor scores were used as the dependent variable in a set of hierarchical linear modeling analyses (or HLM). Akin to multiple regression, HLM also takes into account the nested structure of the data (that is, with observations nested within individual raters). These HLM analyses allow an exploration of the extent to which each regularity predicts aesthetic response, and how these relationships vary across participants who themselves differ in their overall ratings. The technique of HLM is described in more detail later in the dissertation.

The key finding from Experiment 1A is strong influence of a tonic versus non-tonic ending on aesthetic response: melodies that end on the tonic note are rater significant higher than those not ending on the tonic note. This effect is so strong that it appears to overwhelm the effects of the three other melodic regularities. To more sensitively probe for the effects of the other variables, the next few Experiments, 1B and 1C, attempted to control for the overwhelming influence a tonic ending seems to have on people’s perceptions of melodic phrases. Experiment 1B is simply a reanalysis of the data from Experiment 1A, but with trials ending on the tonic analyzed separately from those not ending on the tonic. While this is a step in the right direction when it comes to trying to understand the effects of the remaining regularities, it is possible that the context of providing ratings on trials where tonic and non-tonic endings were intermixed may have influenced the ratings.

Experiment 1C was an attempt to resolve this issue by exposing participants to two separate blocks of melodic phrases. One block consisted of melodic phrases that ended on the tonic, and the other block was melodic phrases that did not end on the tonic. It was thought that these two Studies would show essentially the same results upon analysis; however, the results of Experiments 1B and 1C had some similarities but were not exactly the same. The differences are that with melodic phrases that do end on the tonic, Rule 1 showed an influence in both Experiments 1B and 1C, showing a quadratic effect in Experiment 1B and a linear effect in Experiment 1C. Further, when only hearing melodic phrases that do not end on the tonic, in Experiment 1B, Rule 3 showed an influence on people’s aesthetic ratings, and in Experiment 1C, Rule 2 showed an influence. Again, there is no clear reason why these differences appeared in the two sets of results. However, it seems logical to assume that of the two different sets of results, Experiment 1C would show a clearer picture because experimental participants were exposed to two discrete blocks of phrases, phrases that either did or did not end on the tonic, whereas in Experiment 1B, they heard them all mixed up, exactly as in Experiment 1A. This difference, either being exposed to both melodic phrases that do and do not end on the tonic mixed together in the same block, or in the two types of melodic phrases in two separate blocks, seems the most logical reason for the differences between the results of Experiments 1B and 1C. So in this case, the types of melodic phrases one is hearing at the moment seems to influence the way people aesthetically perceive melodic information.

Experiment 1D was something of a post-script to these studies and represented a further exploration of several different types of non-tonic endings. The main finding here was that listeners do not appear to discriminate between these endings. Rather, the effect of the tonic versus non-tonic ending appears to be very much an all-or-none effect.

In sum, at the very least, Experiments 1A through 1D indicate that, apart from the large positive impact of a tonic (compared to a non-tonic) ending, the remaining three melodic regularities show very subtle effects, which will require additional sophisticated experimental research to better understand.

Next, in Experiment 2, in order to try to further inform the nature of how these melodic regularities are mentally represented, I attempted to determine which of the regularities could be explicitly identified by participants. To do this, participants were exposed to a number of melodies that adhered to all four of the proposed regularities, and after hearing the bank of melodic phrases, they were asked to identify any characteristics that were shared by all the phrases they have just heard. The results showed that 67% of participants were able to identify that each phrase seemed to ascend then descend (Rule 3), and 58% of participants were able to articulate that each phrase ended on the tonic note (Rule 4). The idea here is that if the regularity or combination of regularities influences people’s ratings of well formedness, preference or interestingness, and they are unable to explicate the regularities, then these regularities must be operating on an unconscious or implicit level. In this case, melodic contour did not seem to have a predictable influence in the first set of experiments done here, but the tonic did. Therefore, the tonic ending again appears to influence people's aesthetic ratings and they can generally explicitly specify the occurrence of this regularity in melodic phrases.

In the next study, Experiment 2B, participants were trained on the four regularities, and then asked to decide if a phrase adhered to a particular rule or not. Here, participants were able to accurately decide if a phrase ended on the tonic (Rule 4) 70% of the time. The other three rules showed markedly lower, approximately chance-level, accuracy.

In a final study, Experiment 3, I tried to replicate a finding that previously showed that exposure to initially unpreferred aesthetic stimuli causes people to like them even less (Meskin, Phelan, Moore, & Kieran, 2013). The rationale for this is that in some real-world cases, at least some people come to enjoy even ‘difficult’ aesthetic productions – for instance, the atonal music of Schoenberg, the works of Stravinsky, or free jazz. Is part of this dynamic simply acquiring enough exposure to overcome an initial negative bias? To explore this issue, here I exposed participants to only phrases that did not end on the tonic, since they were shown in Experiment 1A to have the lowest aesthetic ratings. The results showed that although the mean difference in the ratings did not seem to significantly change, the direction of their actual ratings did, as evident by the sign test. In other words, people did rate the melodies lower after being exposed to similar non-tonic ending phrases, but the degree to which they rated them less was not statistically significant. This is broadly in line with Meskin et al.’s (2013) findings for visual art.

These studies collectively show that regarding the nature of people’s mental representations of melodic phrases and the statistical regularities of interest here, people are able to articulate that a phrase ends on the tonic with and without explicit instruction, and also phrases that end on the tonic elicit higher aesthetic ratings. In other words, of the three melodic regularities that are the core topic of this dissertation, a tonic ending appears to be the most different from the others – it has the most potent effect on aesthetic liking, and it is recognized and identified more readily and explicitly than the other three regularities.

These experiments help shed some light on the nature of the mental representations listeners use while engaged in music listening and also help to understand the nature of melodic statistical regularities and how they influence people’s perception of melodic material. As mentioned, these universal regularities have not been previously studied as an aggregate, so understanding whether or not they are interdependent and whether they can be ordered or ranked according to their influential power over people’s preferences and reports of well formedness and interestingness would benefit researchers trying to understand how people develop their preferences and how much power individual composers have over the artistic rules governing their own compositions. In the future, one could imagine analyzing rhythmic components to music the same way melodic components were analyzed here, and even observe the possible differences in mood states and emotions that different combinations of these regularities, and other types of musical regularities, might elicit.